Difference between revisions of "2008 USAMO Problems/Problem 5"
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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 18:58, 1 May 2008
Problem
(Kiran Kedlaya) Three nonnegative real numbers 
, 
, 
are written on a blackboard. These numbers have the property that there exist integers 
, 
, 
, not all zero, satisfying 
. We are permitted to perform the following operation: find two numbers 
, 
on the blackboard with 
, then erase and write 
in its place. Prove that after a finite number of such operations, we can end up with at least one 
on the blackboard.
Solution
Solution 1
Solution 2
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
Resources
| 2008 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
- <url>viewtopic.php?t=202910 Discussion on AoPS/MathLinks</url>
